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Combining features of disco, funk and electronica, the release of the album represented the peak of international commercial success for Jamiroquai, and in the ensuing world tour the group became a household name in many countries. The sleeve art of A Funk Odyssey features Jay Kay posed in front of a series of lasers that form the famous "Buffalo Man" logo, making it the first Jamiroquai album not to feature the logo prominently on its cover. The album marks a departure from the band's previous acid jazz sound; the band finds themselves in a disco funk vibe, and is also very focused on an electronica sound, evident especially in "Twenty Zero One" and "Stop Don't Panic". A popular fan interpretation is that "Main Vein" is a song written about Denise van Outen, Jay's ex-girlfriend, but from her perspective; the song would have thus featured a female vocalist and would showcase the same fight shown in "Little L" but from Denise's perspective. A test pressing of the album features an instrumental of "Main Vein", which supports this theory.

Initial critical response to A Funk Odyssey was generally mixed. At Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream critics, the album has received an average score of 58, based on 13 reviews.[1]Q magazine gave the album 4 out of 5 stars, claiming "A certified thoroughbred. This time, there's a bankable chorus or barbed sentiment for every mirror-ball moment....demonstrating that no-one does sci-fi boogie quite as well as he does sci-fi boogie." They also listed it as one of the best 50 albums of 2001.[6]CMJ described the album as "The perfect mixtape to snap your fingers to on your way to another universe."

"Cannabliss" was a track which was performed live during a pre-album tour in 2001. The track was scrapped from the project after Jay claimed that it wasn't even half complete at the time of going to press. The track's introduction was re-used for "Corner of the Earth". The album's title track, "A Funk Odyssey", was performed by the group while on tour, however, was not included on the album. It is unknown whether this track is an outtake from the album, or was intended as a live-only track. "Shoot The Moon" was a further outtake from the album, performed live at least twice, once at the Montreux Jazz Festival in 2003, and once at a concert in Turkey. A widely circulated recording of the song being played at the festival exists, and can be found on the group's official website for download. One interesting fact about the song is that it was intended to have a horn section. The band did not have a horn section at the time, so the electric guitar had to substitute the horns. A studio version was never recorded. The test pressing of the album also featured three interludes. The first features band frontman Jay in an electronically manipulated monologue, asking himself why he would want to "shut down the funk assembly unit." The second interlude is a beatbox track, which was later sampled in the single "Feels Just Like It Should", while the third features Strauss' "The Blue Danube" being faded in slowly at a low volume. A case of synchronicity occurs when the test pressing is played to Stanley Kubrick's film adaptation of Arthur C. Clarke's 2001: A Space Odyssey.[7]